{"paper":{"title":"A Generalized Trace Reconstruction Problem: Recovering a String of Probabilities","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"cs.DS","authors_text":"Gregory Valiant, Joey Rivkin, Paul Valiant","submitted_at":"2024-12-01T05:06:43Z","abstract_excerpt":"We introduce the following natural generalization of trace reconstruction, parameterized by a deletion probability $\\delta \\in (0,1)$ and length $n$: There is a length $n$ string of probabilities, $S=p_1,\\ldots,p_n,$ and each \"trace\" is obtained by 1) sampling a length $n$ binary string whose $i$th coordinate is independently set to 1 with probability $p_i$ and 0 otherwise, and then 2) deleting each of the binary values independently with probability $\\delta$, and returning the corresponding binary string of length $\\le n$. The goal is to recover an estimate of $S$ from a set of independently "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.00674","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2412.00674/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}